Can DQN announce it has things in its hand in a card game?
The simplest thing to do when you make you first implementation of the agent, is to automate decisions like this, in order to keep representations and decisions simple.

However, if you want to explore tactics surrounding declaration, then I think the following applies:


There should be an initial round of actions where the agent may get to decide whether or not to declare a Ronda, based on the cards it holds. These will be different action choices to playing cards, so you would need to alter your action representation to include those choices. Only allow action choices which are valid, so if it is not valid to declare a Ronda or a Tringa when a player does not have one, then the player does not get to make that choice.
You may want to add a state feature "has a Ronda" and "has a Tringa" for the agent's player, to help with the action decision. 
You should also add a state feature for each player according to whether they declared a Ronda or a Tringa.
Rather than have the agent learn to detect a lie, given your comment that all cards are played so it is easy to tell (there are only 8 cards total in play by the end), then I would just assume lies are automatically found out and include that in the game engine. In other words, the penalty is always paid.
The interesting question is then whether withholding the declaration can give a tactical advantage when the round is being played (because your opponent knows less about your hand), and whether that advantage offsets the inevitable penalty. This might not be true in your card game, but could be true in games with similar choices.



  Could a DQN handle this?


A DQN is maybe going to struggle with partial information in this game. The opponent's cards are hidden from the network, but could have a non-random influence on the opponent's choices of action. It is possible that you will need to investigate agents that can solve POMDPs to get the best player. 

I don't know for certain though. It depends on how much tactical advantage there is in having concealed cards, or how much that is just luck that plays out much the same whether you know the opponent's cards or not. If there is strategy, and ways to determine/guess what the opponent holds based on your cards and their actions so far, this is more like a POMDP.